A heavy cable of length $l$ and linear mass density $\lambda$ (mass/length) hangs vertically from a high bridge. What is the tension in the cable at its midpoint of $l / 2$ ?
A) $g \lambda l$
B) $\frac { 1 } { 4 } g \lambda l ^ { 2 }$
C) $\frac { 1 } { 2 } g \lambda l$
D) $\frac { 1 } { 4 } g \lambda l$

Question

Quizplus · Accepted Answer

The tension in the cable at its midpoint is due to the weight of the half of the cable hanging below that point. Since weight is given by $mg$, where $m$ is the mass of the cable and $g$ is the acceleration due to gravity, and the mass of half the cable is $\frac{\lambda l}{2}$, the tension is $\frac{\lambda l}{2}g$, which simplifies to $\frac{1}{2}g\lambda l$.

A Heavy Cable of Length lll And Linear Mass Density λ\lambdaλ (Mass/length) Hangs Vertically from a High Bridge

A Heavy Cable of Length $l$ And Linear Mass Density $\lambda$ (Mass/length) Hangs Vertically from a High Bridge